Ross Douthat: "If you want a reason why an abortion compromise isn't possible, try this contrast: My idea of a plausible middle ground on the issue requires the overturning of Roe v. Wade, followed by a move toward a system in which abortion is legal but discouraged in, say, the first ten weeks of pregnancy, and basically illegal thereafter." Later: "After all, liberal, well-off, Planned Parenthood-friendly Massachusetts, had a late-'90s abortion rate roughly twice as high as poor, socially-conservative states like Mississippi, Arkansas and Alabama, and more than three times as high as highly pro-life states like South Dakota and Utah."
My hunch is that this discrepancy may have to do with what our current President might refer to as "conditions on the ground". There are only two abortion providers in all of Mississippi, leaving 91% of women in living in counties without a provider, while Massachusetts has the most widespread abortion access in the nation (source, though I believe since 2005 one of the two providers in Mississippi has closed). Arkansas and South Dakota also rank very low on this metric, and while Utah and Alabama fare better, they're not in the top half. Likewise, states where social conservatism is closer to the front of the political issue mix are more likely to adopt measures restricting or deterring access such as "conscience clauses" for pharmacists, "informed consent" rules, and so forth.
But stepping back from the specific question, yes, as Ross points out, if the whole thing is a debate about the rights of the unborn, then there's an impasse. But the challenge for pro-choicers isn't necessarily to accomodate those who think abortion is about the rights of the unborn. Public opinion on abortion is incredibly muddled. The public doesn't want to see Roe v. Wade overturned. But they support most restrictions on abortion that you can come up with. A number of people say that they personally would not choose to have an abortion, but that it should still remain legal. In general, as Atrios likes to say, there are a large number of people who think that abortion should be legal but "think it's icky" and thus our laws should somehow reflect the fact that they think it's icky, and the challenge is to peel those voters away from the GOP, rather than tangle in a debate about at what point a fetus becomes a "person" in the legal sense. If you come out with a policy platform that keeps abortion legal but enacts measures that encourage alternatives or prevent unanticipated pregnancies, it won't win over the Ross Douthats of the world, but there are other quasi-pro-life voters that it might impress.